Cronbach’s α, Revelle’s β, and Mcdonald’s ωH: their relations with each other and two alternative conceptualizations of reliability

Abstract

We make theoretical comparisons among five coefficients—Cronbach’s α, Revelle’s β, McDonald’s ωh, and two alternative conceptualizations of reliability. Though many end users and psychometricians alike may not distinguish among these five coefficients, we demonstrate formally their nonequivalence. Specifically, whereas there are conditions under which α, β, and ωh are equivalent to each other and to one of the two conceptualizations of reliability considered here, we show that equality with this conceptualization of reliability and between α and ωh holds only under a highly restrictive set of conditions and that the conditions under which β equals ωh are only somewhat more general. The nonequivalence of α, β, and ωh suggests that important information about the psychometric properties of a scale may be missing when scale developers and users only report α as is almost always the case

Preparation of this article was supported by the Patricia M Nielsen Research Chair of the Family Institute at Northwestern University